No, you can't. You can use the built-in features of the platform such as adding cards or applying 'Enhancements' (Youtube's terminology, not mine), but there's no way to replace the video itself. From the official documentation:
You can’t replace a video because any new video you upload to YouTube
will get a new URL. Instead, you can make changes to an existing
- Enhance your video: You can make some editorial changes to the video using YouTube Video Enhancements. You can trim parts of your
video, auto-fix lighting and color, blur parts of the video, apply a
filter, and more.
- Add cards to your video: You can use cards to change elements of your videos. You can point viewers to a specific URL (from a list of
eligible sites) and show customized images, titles, and calls to
action, depending on the card type.
- Change your video's title and description: You can organize and make changes to your video's title, category, description, and privacy
If video replacement is a feature you deem necessary for whatever content you are producing, you might consider switching to a hosting platform that allows you to do this. For example, replacing the original video file while keeping views, comments et c. intact is possible on Vimeo (documentation, as of August 2017).